Just my experience, not a guide.... consider this a disclaimer. I tend to eat the same things in the same places that were safe in the past. I am assuming you know the basic guidelines about being gluten free. I avoid foods that may have had contact or "contamination" by gluten.
"Tengo un Alérgica de Trigo,.... un Alérgica de Pan y harina blanco. No puedo comer comidas con Salsa Magi ni Salsa Soya."
Beware of marinades because both Maggi and Soy sauces contain gluten.Bloody Mary's are likely to contain Magi Sauce. Tik n xik fish may have Maggi sauce in the marinade. Some types of Worcestershire sauces contain gluten.
Local corn tortillas from the tortillarias have been safe for me. Among the tostadas sold in bags, most that I have read have been free of wheat flour, but not all..read the labels. There is a possibility that the tostadas served on the table (or in the nachos or chilequiles, etc) were fried in oil that is used to fry items containing wheat. Ask, or avoid them. Places I have asked & done okay include Social Justicia Cocktaileria, Penquinos at Hotel Posada del Mar.
I don't eat at the little restaurants in the nearby colonias that sell flat chicken tacos in different varieties called tostadas, sopes, panuchos, etc.; because their tortillas are cooked in the same pan in the same oil. The tortillas used for sopes have wheat flour added in their masa (Or maybe it is panuchos.) I once brought in a plate with my own tortillas on it and had them add the toppings and they were fine with that. They may have unfried tortillas they could use, but that seemed easy.
I usually eat shrimp rather than fish because it is less likely to be marinated, and I like shrimp. When I want fish I usually have it "en paquete"..which is a filet filled with seafood with a sauce cooked in an aluminum packet called "filete relleno con mariscos". I like Shrimp Diablas, which is usually sauteed in a fresh tomato sauce in a pan with sweet peppers & onion. It is not particularly spicy if you remove the whole chipolte pepper before you start eating. I have eaten both of these at Minino's safely many times, and they seem safe at other places.Vera Cruz is style is also safe there, and generally does not contain gluten. Minino's is a cocteleria on main street/Medina Rudina, north of the gas station. I have ordered these dishes elsewhere with success.
Breakfast at Amigos has consistently gone well and is a favorite of mine; the waiter even remembers I want corn tortillas and not pan tostada. My favorite is the Popeyes omelet and I used to have the Huevos Mexicanas. They are making their own hash browns again, which are very good. (During the months they had a fried frozen triangle I avoided it, because frozen potatoes often contain gluten..and are often fried in "community oil" fryers, so I never eat them out.)Amigos in on Hidalgo, about midway.
For breakfast I often have a fruit bowl. I also have Huevos Mexicanas at either Poc Chuc restaurant, where I like their fruit bowls also. (There is one on Juarez & Matamoris and another at the Mercado on Guerrero..which has been renamed Letty's. ) My recent 'breakfast bowl' at Lola Valentina's is a new favorite.
I have eaten safely at Medina's taqueria for years, where I usually have chicken tacos. I have also enjoyed their tacos al pastor & their charros especial, which include pastor. (Tho they are kinda salty) Pastor is marinated pork cooked on a rotisserie, and they slice off the crispy outer bits when you order. This marinade usually also involves achiote and bitter limon. Charros are beans rancheros. They are on the north end of Hidalgo and in the evenings/nights.
Lola Valentina's staff is gluten-aware & bilingual, and I have have eaten there several times and done fine; as well as having confidence that I was understood.
Qubano's moved in nearby where the previous Cuban restaurant was, and Vivian is also gluten aware & I enjoyed a tostone chicken sandwich there, with no reaction. They are both on the north end of Hidalgo.
Varadera, the Cuban Restaurant near Chuuk Kay has shrimp & fish grilled simply that are gluten free and very tasty. I recommend the mojitos also
Penguino's at Posada del Mar has prepared Gluten free food for me. Their tostadas are safe (they also have excellent mojitos). The seafood dinner for two was Really Good.
Be careful about rice or soups which can contain gluten from bouillon. This may also be true of Chilequilles. Maggi bouillon is gluten free, Knorr is not.
Be careful about cochinita pibil...some cooks marinate it with beer. Be careful of ANYTHING that may be marinated unless you know all the marinade ingredients are GF.
There are many other options I am making no guarantees, just sharing my experiences. At a new restaurant I usually ask about something simple, like grilled fish or shrimp...and specifically check about marinades, and explain about 'contamination'. I often go chat with the waiter when he is NOT in the middle of taking orders.